A brief discussion of talbot effect and moire pattern.

1. ESTIMATION OF FOCAL LENGTH OF LENSES
USING
TALBOT INTERFEROMETRY
SUBMITTED BY
GEETHU KRISHNA
REG NO: 63017143003
UNDER THE GUIDANCE OF
DR. SIVARAMA KRISHNAN
ASSOCIATE PROFESSOR
DEPT. PHYSICS
IITM CHENNAI

2. CONTENTS
• Interference
• Interferometry
• Talbot Effect
• Moirѐ Pattern
• Experimental details, optical components and equipment's
• Method used for collimating the laser beam
• Method to find the pitch of the grating
• Method used to find the focal length of lenses
• Result and discussion
• Merits and Demerits of the technique
• Future Scope

3. INTERFERENCE
 The phenomenon of redistribution of energy due to super position of light waves from coherent sources
is called Interference.
 Types of Interference
Constructive Interference Destructive Interference

4. INTERFEROMETRY
 Interferometry is a measurement method which employs the phenomenon of interference of waves.
 Interferometers are investigative tools of Interferometry.
 In this study we focus on the measurement of pitch of a grating and the focal length of lens using
Talbot Interferometry

5. TALBOT EFFECT
 The Talbot effect is a diffraction effect first observed in 1836 by Henry Fox Talbot.
 Referred to as self-imaging or lens less imaging, in which a periodic structure can produce self-
images at certain regular distances.
 When a plane wave is incident upon a periodic diffraction grating, the image of the grating is
repeated at regular distances away from the grating plane, known as Talbot Distance

6. The optical Talbot effect for monochromatic light, shown
as a "Talbot carpet"

7. MOIRЀ PATTERN
 It refers to a beat pattern produced between two gratings of approximately equal spacing.

8. OPTICAL COMPONENTS AND EQUIPMENT'S
LENS RONCHI GRATING HE-NE LASER

9. CHARGED COUPLED DEVICE (CCD) TRAVELLING MICROSCOPE
Experimental Setup of Talbot Interferometry

10. METHOD USED FOR COLLIMATING THE
LASER BEAM

11. METHOD TO FIND THE PITCH OF THE
GRATING
Objective lens Collimating lens CCDGrating
Pitch, p =
𝜆𝐷
𝑚
were m: order of the Talbot image
λ: wavelength of the source
D: distance between the gratings.

12. METHOD USED TO FIND THE FOCAL LENGTH
OF LENSES

13. Focal length, f =
𝑚1
𝑠𝑖𝑛𝜃𝑡𝑎𝑛𝛼 𝑎+𝑐𝑜𝑠𝜃−1
𝑚𝑝2
𝜆
𝜃: tilt angle between Gratings.
αa: Angle between Fringes before and after lens insertion.
p: Pitch of grating.

14. RESULT AND DISCUSSION
Grating Order(m) Self-imaging Wave(nm) Pitch (p)
Pitch
calculated
using Talbot
Interferometry % Error
1 1 6.366 632.8 2.0020×10-4 2.02×10-4 0.89
2 1 6.396 632.8 2.0404×10-4 2.00×10-4 2.02
3 1 3.112 632.8 1.4033×10-4 1.41×10-4 0.47
3 2 6.190 632.8 1.3990×10-4 1.41×10-4 0.78
4 2 3.439 632.8 1.0431×10-4 1.00×10-4 4.31
4 3 4.962 632.8 1.0230×10-4 1.00×10-4 2.30
4 4 6.592 632.8 1.0212×10-4 1.00×10-4 2.12
 PITCH IS ESTIMATED

15. Lens Tilt angle Focal length(cm) Power (D) Percentage Error
1 138.4 -1.0099 -0.9902 0.99
2 119.1 -0.5015 -1.99402 0.3
3 110.3 -0.3338 -2.99581 0.14
4 105.5 -0.2505 -3.99202 0.2
5 102.5 -0.2003 -4.99251 0.15
 Estimated focal length values of Concave lens

16.  Estimated focal length values of Concave lens
Lens Tilt angle Focal length(cm) Power (D) Percentage error
1 130.5 -1.0089 -0.99118 0.88
2 101.8 -0.2509 -3.98565 0.37
3 113.12 -0.5099 -1.96117 1.95
4 105.5 -0.3325 -3.00752 0.25
5 99.4 -0.2012 -4.97018 0.6

17. Lens Tilt angle
αa
Focal length(cm)
f
Power (D) Percentage Error
1 42.6 0.9941 1.005935 0.59
2 60.9 0.5064 1.974724 1.26
3 69.83 0.3336 2.997602 0.08
4 74.58 0.2503 3.995206 0.12
5 77.55 0.2003 4.992511 0.15
 Estimated focal length values of Convex lens

18. MERITS AND DEMERITS OF THE TECHNIQUE
 Merits
The optical system is simple and the sensitivity can be easily tuned by choosing the Talbot
length for the distance between the two gratings.
We can measure focal length of both positive and negative lenses with the same optical
system.
Installation is easy.
 Demerits
Length of the optical bench is limited.
Measuring device for the angle is not appropriate.

19. FUTURE SCOPE
 The phenomenon of self-imaging has application in other research fields, such as cold
atoms/molecules, waveguides, x ray, acoustics, plasmonic, and Bose–Einstein condensates.
 Talbot effect is an important optical element that has wide scope in optical inter connection optical
communication and optical computing.
 Talbot effect is in cooperated with the Moirѐ pattern for further studies which paved the way for
medical imaging and non-destructive testing

20. THANK YOU